Using Student-Response Systems in Entry-Level College ... · Use the product, quotient, zero exponent, negative exponent, power, and special product rules for exponents in order to

S

Using Student-Response Systems in Entry-Level College Mathematics

Courses

NCTM Regional Conference, Louisville, KY

November 7, 2013

Jonathan Engelman, MAKettering College

[email protected]

Tuesday, November 5, 13

mailto:[email protected]


Roadmap

S Formative Assessment

S What are clickers?

S One clicker sequence, with results

S Debrief

S Plethora of example questions

2


What is the goal of teaching?


The Three Questions:



S 1. Where is the learner right now?




S 2. Where is the learner going?




S 2. Where is the learner going?

S 3. How will the learner get there?


Formative Assessment Characteristics



S 1. Intended outcomes of learning are clearly stated and shared




S 2. Designed to collect quality evidence to inform teaching and improve learning





S 3. Formative feedback to improve learning is provided to each student





S 3. Formative feedback to improve learning is provided to each student

S 4. Students are engaged in the assessment process and, to the extent possible, in planning their own next steps for learning


S

QuestioningAn Assessment for Learning Strategy


3 Things to Take Away About Questioning

S Plan questions ahead of time

S Questions directly connect to lesson objectives

S Leave enough time for students to think, respond to the prompt, and respond to one another


Planning Your Questions

S Previous Material/Warm Up Questions:

S Pre-Assessment Questions

S Engagement Questions

S Checking for Understanding Questions

S Wrap Up Questions


Clickers in 30 Seconds

9


Clicker Questions

S Three types:S Multiple ChoiceS NumericS Alpha Numeric

S Can be timed or un-timed

S Can be scored for correctness or participation

10


Example Sequence: Exponents

S Use the product, quotient, zero exponent, negative exponent, power, and special product rules for exponents in order to simplify them.

S Use order of operations to simplify real number expressions containing exponents

11


Critical Thinking Question

SSimplify:

12

(�3)2



13


Note

SThe following question was added after section 1 and before sections 3 and 4

14



SSimplify:

15

�32



16



SSimplify:

17

x

7

x

�4



18



S vs SA) Both -16SB) Both 16SC) 16, -16SD) -16, 16SE) None of the above

19

�24 (�2)4



20



21


Debrief

S What did you notice about this questioning strategy?

S What worked about the strategy?

S When could this strategy be useful?

S How might you implement the strategy in your class?

S http://mathquest.carroll.edu/


http://mathquest.carroll.edu/

http://mathquest.carroll.edu/

Debrief: Formative Assessment

S Asking questions that point toward the goal/s for the day

S Change instruction based on results

S Class discussion: “Why is that the right answer?”

23


Questioning “on the Fly”

S Wait time – first and second

S How can the prompts we developed in the first strategy help you increase your wait time?

S “what do others think?”S “how do you know if that is true or not?”S “who can add on to what Lindsay just said?”


Pitfalls

S How much time to spend on each question?

S Cost of technology

S Multiple choice questions

25


Resource

26


Resource

27


Resource

28


Resource

29


Questions?

S [email protected]






Bonus Questions

31



SConvert 8 m to mm:SA) 0.08 mmSB) 0.8 mmSC) 80 mmSD) 800 mmSE) 8000 mm

32



SConvert 7.68 kg to pounds. Round to 2 decimal placesSA) 3.48 lbSB) 3.49 lbSC) 16.90 lbSD) 16.91 lbSE) None of the above

33



STrue or False: 1 is a prime number.SA) TrueSB) False

34



SFind the GCF of 360 and 1350.

35



SFill in the blank: -4____-(-5)SA) >SB) <SC) SD) SE) =

36

�



SSimplify without using a calculator:

37

(�10 + 4) · (�3)

�7� 2



SSimplify without using a calculator:

38

21

5÷ 7

15



SSimplifySA) SB) SC) SD) SE)

39

p32p

322p16

16p2

4p2

2p4



SSolve: -(9-3x)-(4+2x)-4=-(2-5x)-x

40



S In a chemistry class, 12 liters of a 12% alcohol solution must be mixed with a 20% solution to get a 14% solution. How many liters of the 20% solution are needed?

41



S The weight of an object above Earth varies inversely as the square of its distance from the center of Earth. If an astronaut in a space vehicle weights 57 pounds when 6700 miles from the center of Earth, what does the astronaut weight when 4090 miles from the center?

42



43

Factor: 2x

2+ x� 36

A) (2x� 4)(x+ 9)

B) (x+ 4)(2x� 9)

C) (2x+ 4)(x� 9)

D) (x� 4)(2x+ 9)

E) None of the Above

Factor: 25x

2 � 20x+ 4

A) (5x� 1)(5x� 4)

B) (5x+ 1)(5x+ 4)

C) (5x� 2)

2

D) (5x+ 2)

2


Factor: x

4 � 1

A) (x� 1)(x+ 1)(x

2+ 1)

B) (x

2 � 1)(x

2+ 1)

C) (x� 1)(x+ 1)

3

D) (x� 1)

2(x+ 1)

2


Factor: x

3 � 27

A) (x� 3)(x3)2

B) (x� 3)(x

2+ 3x+ 9)

C) (x� 3)

2(x+ 3)

D) (x� 3)(x+ 3)(x+ 9)


1



SFor any value of x, the point (x,0) lies on the _____-axis.

44



SFor any value of y, the point (0,y) lies on the _____-axis.

45



SCalculate the slope between the points (-4,3) and (-3,4).

46



SWrite the slope-intercept form of the equation of the line passing through (5,8) with a slope of -2.

47



SFind the slope of the line perpendicular to 2x+3y=6.

48



Does the graph of the function open up or down?

A) Up

D) Down

f(x) = x

2 + 2x+ 6



What is the equation for the axis of symmetry for the function?

f(x) = x

2 + 2x+ 6



What is the y-coordinate of the vertex of the function?

f(x) = x

2 + 2x+ 6



What is the y-coordinate of the y-intercept of the function?

f(x) = x

2 + 2x+ 6



What are the x-intercepts of the function?

A) x=2,3

B) x=-2,-3

C) x=-2,3

D) x=2,-3

E) No solution

f(x) = x

2 + 2x+ 6



What is the domain of the function?

f(x) = x

2 + 2x+ 6



What is the range of the function?

f(x) = x

2 + 2x+ 6



S If $20,000 is invested at 3% annual interest, how much money, to the nearest cent, is in the account after 4 years if compounded continuously?

56



S Which of the following ordered pairs is a solution to the system?

S -2x+3y=11 and -2x+2y=4S A) (-4,1)S B) (1,3)S C) (5,7)S D) (-1,3)S E) None of the above

57



SFind the angle of least positive measure that is coterminal with:

58

539�



SFind if .

59

csc ✓ sin ✓ =2

3



SUse identities to find if with in quad. IV.

60

sec ✓ sin ✓ = �p3

2✓



S Given a triangle with angles A, B, and C, and opposite sides a, b, and c, find the measurements of the remaining angle and sides assuming that B=30 degrees, C=100 degrees, and b=20 ft.S A) A=50 degrees, c=39.39 ft, a=30.64 ftS B) A=50 degrees, a=10.5 ft, c=20.26 ftS C) A=50 degrees, a=30.64 ft, c=30.64 ftS D) A=230 degrees, a=30.64 ft, c=39.39 ftS E) None of the above

61



SFind the (arithmetic mean, median, mode, range, midrange, standard deviation) of the following set of data:S10,8,11,11,11,13,15

62



SA coin is flipped three times in a row. What is the probability of getting 3 tails in a row?

63



S If a single die is rolled, what is the probability of a 2 or an odd face coming up? Round your answer to three decimal places.

64



SA jar contains 4 red spheres, 3 blue spheres, and 2 yellow spheres. Two spheres are drawn without replacement. Find the probability that a yellow sphere is drawn and then a blue ball, in that order. Round your answer to three decimal places.

65



SEvaluate the expression for x=3 and y=-5.

66

x� 3y

2+ xy



• Evaluate the expression:

• A)

• B)

• C)

• D)

• E) None of the above

x

�2y

3z

�4

x

�3y

5z

5

x

2/3y

3/5z

�4/5

xy

2z

9

x

�5y

8z

x

y

2z

9



68

Factor: 2x

2+ x� 36

A) (2x� 4)(x+ 9)

B) (x+ 4)(2x� 9)

C) (2x+ 4)(x� 9)

D) (x� 4)(2x+ 9)


Factor: 25x

2 � 20x+ 4

A) (5x� 1)(5x� 4)

B) (5x+ 1)(5x+ 4)

C) (5x� 2)

2

D) (5x+ 2)

2


Factor: x

4 � 1

A) (x� 1)(x+ 1)(x

2+ 1)

B) (x

2 � 1)(x

2+ 1)

C) (x� 1)(x+ 1)

3

D) (x� 1)

2(x+ 1)

2


Factor: x

3 � 27

A) (x� 3)(x3)2

B) (x� 3)(x

2+ 3x+ 9)

C) (x� 3)

2(x+ 3)

D) (x� 3)(x+ 3)(x+ 9)


1



69

Factor: 2x

2+ x� 36

A) (2x� 4)(x+ 9)

B) (x+ 4)(2x� 9)

C) (2x+ 4)(x� 9)

D) (x� 4)(2x+ 9)


Factor: 25x

2 � 20x+ 4

A) (5x� 1)(5x� 4)

B) (5x+ 1)(5x+ 4)

C) (5x� 2)

2

D) (5x+ 2)

2


Factor: x

4 � 1

A) (x� 1)(x+ 1)(x

2+ 1)

B) (x

2 � 1)(x

2+ 1)

C) (x� 1)(x+ 1)

3

D) (x� 1)

2(x+ 1)

2


Factor: x

3 � 27

A) (x� 3)(x3)2

B) (x� 3)(x

2+ 3x+ 9)

C) (x� 3)

2(x+ 3)

D) (x� 3)(x+ 3)(x+ 9)


1



SMultiply and simplify:

70

x� 3

2x+ 4· 10x+ 20

5x� 15



• Simplify:

• A)

• B)

• C)

• D)

• E)

✓x

�1/4

y

�2/3

◆�12

⇣y

x

⌘11

y

18

x

48

x

48

y

18

x

3

y

8

y

8

x

3



SSimplify:

72

2 +p�4

1 + i



S If (x-2)(x+1)=10, thenSA) x-2=10 or x+1=10SB) x=4 or x=-3SC) x=2 or x=-1SD) x=5 or x=-2SE) None of the above

73



SSolve and check your answer:

74

p6y � 11 = 2y � 7


CRITICAL THINKING QUESTION

Solve the inequality:

A)

B)

C)

D)

E) None of the above

4 < 2� 2x 14

�1 > x � �6

1 > x � �6

�2 > x � �12

�1 > x � �12



A diameter of a circle has endpoints (4,-3) and (-2,5). What is the equation of this circle?

A)

B)

C)

D)

E) None of the above

(x� 1)2 + (y � 1)2 = 10

(x� 1)2 + (y � 1)2 = 25

(x+ 1)2 + (y + 1)2 = 100

(x� 3)2 + (y + 1)2 = 10



S Are the given lines parallel, perpendicular, or neither?

S Line 1: 2x+4y=12

S Line 2: 2x-y=4S A) ParallelS B) PerpendicularS C) Neither

77



STrue or false: If a and b are in the domain of f(x)=1/x, then a+b is also in the domain of f(x).SA) TrueSB) False

78



True or False: The function is an odd function.

D) False

B) True

f(x) = x

3 + x+ 1



STrue or False: The graph of y=f(x) and y=f(-x) cannot be the same.SA) TrueSB) False

80



True or False: You get the same graph by shifting the graph of two units up, reflecting the shifted graph in the x-axis or by reflecting the graph of in the x-axis, and then shifting the reflected graph up two units.

D) True

E) False

y = x

2

y = x

2



STrue or False: The functions f and g are inverses of each other:

SA) TrueSB) False

82

f(x) = g(x) =1x



STrue or False:

SA) TrueSB) False

83

loga(u+ v) = loga u+ loga v


Clicker Question

The terminal side of in standard position contains the given point. Find the exact value of .

(-3,4)

✓

csc(✓)



85


Documents

Using Student-Response Systems in Entry-Level College ... · Use the product, quotient, zero exponent, negative exponent, power, and special product rules for exponents in order to